Effect of idler absorption in pulsed optical parametric oscillators

Gunnar Rustad; Gunnar Arisholm; Øystein Farsund

doi:10.1364/OE.19.002815

Effect of idler absorption in pulsed optical parametric oscillators

Gunnar Rustad, Gunnar Arisholm, and Øystein Farsund

Optics Express
Vol. 19,
Issue 3,
pp. 2815-2830
(2011)
•https://doi.org/10.1364/OE.19.002815

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Gunnar Rustad, Gunnar Arisholm, and Øystein Farsund, "Effect of idler absorption in pulsed optical parametric oscillators," Opt. Express 19, 2815-2830 (2011)

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Related Topics
Table of Contents Category
- Nonlinear Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Harmonic generation and mixing (190.2620)
- Nonlinear optics, parametric processes (190.4410)
- Parametric oscillators and amplifiers (190.4970)

About this Article
History
- Original Manuscript: December 20, 2010
- Revised Manuscript: January 19, 2011
- Manuscript Accepted: January 19, 2011
- Published: January 28, 2011

Accessible

Open Access

Abstract

Absorption at the idler wavelength in an optical parametric oscillator (OPO) is often considered detrimental. We show through simulations that pulsed OPOs with significant idler absorption can perform better than OPOs with low idler absorption both in terms of conversion efficiency and beam quality. The main reason for this is reduced back conversion. We also show how the beam quality depends on the beam width and pump pulse length, and present scaling relations to use the example simulations for other pulsed nanosecond OPOs.

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References

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|
Year
|
Author
|
Publication

G. Arisholm, E. Lippert, G. Rustad, and K. Stenersen, “Efficient conversion from 1 to 2 µm by a KTP-based ring optical parametric oscillator,” Opt. Lett. 27(15), 1336–1338 (2002).
[Crossref]
G. Arisholm, Ø. Nordseth, and G. Rustad, “Optical parametric master oscillator and power amplifier for efficient conversion of high-energy pulses with high beam quality,” Opt. Express 12(18), 4189–4197 (2004).
[Crossref] [PubMed]
G. T. Moore and K. Koch, “Efficient high-gain two-crystal optical parametric oscillator,” IEEE J. Quantum Electron. 31(5), 761–768 (1995).
[Crossref]
D. D. Lowenthal, “CW periodically poled LiNbO3 optical parametric oscillator model with strong idler absorption,” IEEE J. Quantum Electron. 34(8), 1356–1366 (1998).
[Crossref]
S. C. Lyons, G. L. Oppo, W. J. Firth, and J. R. M. Barr, “Beam-quality studies of nanosecond singly resonant optical parametric oscillators,” IEEE J. Quantum Electron. 26(5), 541–549 (2000).
[Crossref]
G. Arisholm, R. Paschotta, and T. Sudmeyer, “Limits to the power scalability of high-gain optical parametric amplifiers,” J. Opt. Soc. Am. B 21(3), 578–590 (2004).
[Crossref]
W. Koechner, Solid-state laser engineering (Springer, New York, 1999).
G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14(10), 2543–2549 (1997).
[Crossref]
G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16(1), 117–127 (1999).
[Crossref]
G. Arisholm and K. Stenersen, “Optical parametric oscillator with non-ideal mirrors and single- and multi-mode pump beams,” Opt. Express 4(5), 183–192 (1999).
[Crossref] [PubMed]
Ø. Farsund, G. Arisholm, and G. Rustad, “Improved beam quality from a high energy optical parametric oscillator using crystals with orthogonal critical planes,” Opt. Express 18(9), 9229–9235 (2010).
[Crossref] [PubMed]
A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[Crossref]
G. Arisholm, G. Rustad, and K. Stenersen, “Importance of pump-beam group velocity for backconversion in optical parametric oscillators,” J. Opt. Soc. Am. B 18(12), 1882–1890 (2001).
[Crossref]
A. V. Smith, “Bandwidth and group-velocity affects in nanosecond optical parametric amplifiers and oscillators,” J. Opt. Soc. Am. B 22(9), 1953–1965 (2005).
[Crossref]
G. Hansson, H. Karlsson, S. Wang, and F. Laurell, “Transmission measurements in KTP and isomorphic compounds,” Appl. Opt. 39(27), 5058–5069 (2000).
[Crossref]
W. J. Alford and A. V. Smith, “Wavelength variation of the second-order nonlinear coefficients of KNbO3, KTIOPO4, KTiOAsO4, LiNBO3, LiO3, β-BaB2O4, KH2PO4, and LiB3O5 crystals: a test of Miller wavelength scaling,” J. Opt. Soc. Am. B 18(4), 524–533 (2001).
[Crossref]
L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33(10), 1663–1672 (1997).
[Crossref]
I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]
R. C. Miller, “Optical second harmonic generation in piezo-electric crystals,” Appl. Phys. Lett. 5(1), 17–19 (1964).
[Crossref]
B. C. Johnson, V. J. Newell, J. B. Clark, and E. S. McPhee, “Narrow-bandwidth low-divergence optical parametric oscillator for nonlinear frequency-conversion applications,” J. Opt. Soc. Am. B 12(11), 2122–2127 (1995).
[Crossref]
A. V. Smith and M. S. Bowers, “Image-rotating cavity designs for improved beam quality in nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 18(5), 706–713 (2001).
[Crossref]
R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions,” Opt. Express 14(13), 6069–6074 (2006).
[Crossref] [PubMed]

S. C. Lyons, G. L. Oppo, W. J. Firth, and J. R. M. Barr, “Beam-quality studies of nanosecond singly resonant optical parametric oscillators,” IEEE J. Quantum Electron. 26(5), 541–549 (2000).
[Crossref]

1999 (2)

G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16(1), 117–127 (1999).
[Crossref]

G. Arisholm and K. Stenersen, “Optical parametric oscillator with non-ideal mirrors and single- and multi-mode pump beams,” Opt. Express 4(5), 183–192 (1999).
[Crossref] [PubMed]

1998 (1)

D. D. Lowenthal, “CW periodically poled LiNbO3 optical parametric oscillator model with strong idler absorption,” IEEE J. Quantum Electron. 34(8), 1356–1366 (1998).
[Crossref]

1997 (3)

G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14(10), 2543–2549 (1997).
[Crossref]

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33(10), 1663–1672 (1997).
[Crossref]

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]

1995 (2)

G. T. Moore and K. Koch, “Efficient high-gain two-crystal optical parametric oscillator,” IEEE J. Quantum Electron. 31(5), 761–768 (1995).
[Crossref]

B. C. Johnson, V. J. Newell, J. B. Clark, and E. S. McPhee, “Narrow-bandwidth low-divergence optical parametric oscillator for nonlinear frequency-conversion applications,” J. Opt. Soc. Am. B 12(11), 2122–2127 (1995).
[Crossref]

1990 (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[Crossref]

1964 (1)

R. C. Miller, “Optical second harmonic generation in piezo-electric crystals,” Appl. Phys. Lett. 5(1), 17–19 (1964).
[Crossref]

Alford, W. J.

Arisholm, G.

G. Arisholm, R. Paschotta, and T. Sudmeyer, “Limits to the power scalability of high-gain optical parametric amplifiers,” J. Opt. Soc. Am. B 21(3), 578–590 (2004).
[Crossref]

G. Arisholm, E. Lippert, G. Rustad, and K. Stenersen, “Efficient conversion from 1 to 2 µm by a KTP-based ring optical parametric oscillator,” Opt. Lett. 27(15), 1336–1338 (2002).
[Crossref]

G. Arisholm, G. Rustad, and K. Stenersen, “Importance of pump-beam group velocity for backconversion in optical parametric oscillators,” J. Opt. Soc. Am. B 18(12), 1882–1890 (2001).
[Crossref]

G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16(1), 117–127 (1999).
[Crossref]

G. Arisholm and K. Stenersen, “Optical parametric oscillator with non-ideal mirrors and single- and multi-mode pump beams,” Opt. Express 4(5), 183–192 (1999).
[Crossref] [PubMed]

G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14(10), 2543–2549 (1997).
[Crossref]

Barr, J. R. M.

Bosenberg, W. R.

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33(10), 1663–1672 (1997).
[Crossref]

Bowers, M. S.

A. V. Smith and M. S. Bowers, “Image-rotating cavity designs for improved beam quality in nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 18(5), 706–713 (2001).
[Crossref]

Clark, J. B.

Farsund, Ø.

Firth, W. J.

Hansson, G.

G. Hansson, H. Karlsson, S. Wang, and F. Laurell, “Transmission measurements in KTP and isomorphic compounds,” Appl. Opt. 39(27), 5058–5069 (2000).
[Crossref]

Ito, R.

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]

Johnson, B. C.

Karlsson, H.

G. Hansson, H. Karlsson, S. Wang, and F. Laurell, “Transmission measurements in KTP and isomorphic compounds,” Appl. Opt. 39(27), 5058–5069 (2000).
[Crossref]

Kitamoto, A.

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]

Koch, K.

G. T. Moore and K. Koch, “Efficient high-gain two-crystal optical parametric oscillator,” IEEE J. Quantum Electron. 31(5), 761–768 (1995).
[Crossref]

Kondo, T.

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]

Laurell, F.

G. Hansson, H. Karlsson, S. Wang, and F. Laurell, “Transmission measurements in KTP and isomorphic compounds,” Appl. Opt. 39(27), 5058–5069 (2000).
[Crossref]

Lippert, E.

G. Arisholm, E. Lippert, G. Rustad, and K. Stenersen, “Efficient conversion from 1 to 2 µm by a KTP-based ring optical parametric oscillator,” Opt. Lett. 27(15), 1336–1338 (2002).
[Crossref]

Lowenthal, D. D.

D. D. Lowenthal, “CW periodically poled LiNbO3 optical parametric oscillator model with strong idler absorption,” IEEE J. Quantum Electron. 34(8), 1356–1366 (1998).
[Crossref]

Lyons, S. C.

McPhee, E. S.

Miller, R. C.

R. C. Miller, “Optical second harmonic generation in piezo-electric crystals,” Appl. Phys. Lett. 5(1), 17–19 (1964).
[Crossref]

Moore, G. T.

G. T. Moore and K. Koch, “Efficient high-gain two-crystal optical parametric oscillator,” IEEE J. Quantum Electron. 31(5), 761–768 (1995).
[Crossref]

Myers, L. E.

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33(10), 1663–1672 (1997).
[Crossref]

Newell, V. J.

Nordseth, Ø.

Oppo, G. L.

Paschotta, R.

R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions,” Opt. Express 14(13), 6069–6074 (2006).
[Crossref] [PubMed]

G. Arisholm, R. Paschotta, and T. Sudmeyer, “Limits to the power scalability of high-gain optical parametric amplifiers,” J. Opt. Soc. Am. B 21(3), 578–590 (2004).
[Crossref]

Rustad, G.

G. Arisholm, E. Lippert, G. Rustad, and K. Stenersen, “Efficient conversion from 1 to 2 µm by a KTP-based ring optical parametric oscillator,” Opt. Lett. 27(15), 1336–1338 (2002).
[Crossref]

G. Arisholm, G. Rustad, and K. Stenersen, “Importance of pump-beam group velocity for backconversion in optical parametric oscillators,” J. Opt. Soc. Am. B 18(12), 1882–1890 (2001).
[Crossref]

Shirane, M.

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]

Shoji, I.

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[Crossref]

Smith, A. V.

A. V. Smith, “Bandwidth and group-velocity affects in nanosecond optical parametric amplifiers and oscillators,” J. Opt. Soc. Am. B 22(9), 1953–1965 (2005).
[Crossref]

A. V. Smith and M. S. Bowers, “Image-rotating cavity designs for improved beam quality in nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 18(5), 706–713 (2001).
[Crossref]

Stenersen, K.

G. Arisholm, E. Lippert, G. Rustad, and K. Stenersen, “Efficient conversion from 1 to 2 µm by a KTP-based ring optical parametric oscillator,” Opt. Lett. 27(15), 1336–1338 (2002).
[Crossref]

G. Arisholm, G. Rustad, and K. Stenersen, “Importance of pump-beam group velocity for backconversion in optical parametric oscillators,” J. Opt. Soc. Am. B 18(12), 1882–1890 (2001).
[Crossref]

G. Arisholm and K. Stenersen, “Optical parametric oscillator with non-ideal mirrors and single- and multi-mode pump beams,” Opt. Express 4(5), 183–192 (1999).
[Crossref] [PubMed]

Sudmeyer, T.

G. Arisholm, R. Paschotta, and T. Sudmeyer, “Limits to the power scalability of high-gain optical parametric amplifiers,” J. Opt. Soc. Am. B 21(3), 578–590 (2004).
[Crossref]

Wang, S.

G. Hansson, H. Karlsson, S. Wang, and F. Laurell, “Transmission measurements in KTP and isomorphic compounds,” Appl. Opt. 39(27), 5058–5069 (2000).
[Crossref]

Appl. Opt. (1)

G. Hansson, H. Karlsson, S. Wang, and F. Laurell, “Transmission measurements in KTP and isomorphic compounds,” Appl. Opt. 39(27), 5058–5069 (2000).
[Crossref]

Appl. Phys. Lett. (1)

R. C. Miller, “Optical second harmonic generation in piezo-electric crystals,” Appl. Phys. Lett. 5(1), 17–19 (1964).
[Crossref]

IEEE J. Quantum Electron. (4)

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33(10), 1663–1672 (1997).
[Crossref]

G. T. Moore and K. Koch, “Efficient high-gain two-crystal optical parametric oscillator,” IEEE J. Quantum Electron. 31(5), 761–768 (1995).
[Crossref]

D. D. Lowenthal, “CW periodically poled LiNbO3 optical parametric oscillator model with strong idler absorption,” IEEE J. Quantum Electron. 34(8), 1356–1366 (1998).
[Crossref]

J. Opt. Soc. Am. B (9)

G. Arisholm, R. Paschotta, and T. Sudmeyer, “Limits to the power scalability of high-gain optical parametric amplifiers,” J. Opt. Soc. Am. B 21(3), 578–590 (2004).
[Crossref]

G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14(10), 2543–2549 (1997).
[Crossref]

G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16(1), 117–127 (1999).
[Crossref]

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]

G. Arisholm, G. Rustad, and K. Stenersen, “Importance of pump-beam group velocity for backconversion in optical parametric oscillators,” J. Opt. Soc. Am. B 18(12), 1882–1890 (2001).
[Crossref]

A. V. Smith, “Bandwidth and group-velocity affects in nanosecond optical parametric amplifiers and oscillators,” J. Opt. Soc. Am. B 22(9), 1953–1965 (2005).
[Crossref]

A. V. Smith and M. S. Bowers, “Image-rotating cavity designs for improved beam quality in nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 18(5), 706–713 (2001).
[Crossref]

Opt. Express (4)

R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions,” Opt. Express 14(13), 6069–6074 (2006).
[Crossref] [PubMed]

G. Arisholm and K. Stenersen, “Optical parametric oscillator with non-ideal mirrors and single- and multi-mode pump beams,” Opt. Express 4(5), 183–192 (1999).
[Crossref] [PubMed]

Opt. Lett. (1)

G. Arisholm, E. Lippert, G. Rustad, and K. Stenersen, “Efficient conversion from 1 to 2 µm by a KTP-based ring optical parametric oscillator,” Opt. Lett. 27(15), 1336–1338 (2002).
[Crossref]

Proc. SPIE (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[Crossref]

Other (1)

W. Koechner, Solid-state laser engineering (Springer, New York, 1999).

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Fig. 1

Sketch of OPO geometry assumed in the simulations.

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Fig. 10

a) Comparison of performance of OPOs with small (black curves) and large (red curves) pump group velocity mismatch for no (solid curves) and large (dashed curves) idler absorption with W = 0.5 mm and t_p = 10 ns. b) Signal spectral for the same cases for η ≈ 0.35 for zero idler absorption and η ≈ 0.5 for α = 300 m⁻¹.

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Fig. 2

Overview of the simulated points in the parameter space.

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Fig. 3

a) Signal conversion efficiency (solid curves) and beam quality (dashed curves) as functions of d_eff for different idler absorption levels (units m⁻¹) for W = 0.5 mm and t_p = 10 ns. b) Signal beam quality and conversion efficiency as a parametric plot with d_eff as parameter for different idler absorption for the same OPO as in a). The gray curve connects the points with d_eff = 16 pm/V. The d_eff -values for the other points are listed in the text.

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Fig. 4

Simulation results for 0.5 mm beam radius for varying pump pulse length, as indicated in the graphs. Similar results for 10 ns pulse length were shown in Fig. 3b.

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Fig. 5

Comparison of OPO performance for fixed idler absorption at different pump pulse lengths for 0.5 mm pump beam radius.

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Fig. 6

Simulation results for 10 ns pulse length varying the beam radius as indicated in the graphs. The corresponding graph for W = 0.5 mm is shown in Fig. 3b.

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Fig. 7

Comparison of OPO performance for fixed absorption levels for varying pump beam width for 10 ns pulse width.

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Fig. 8

Comparison of OPO performance in the case of 2 ns pump pulse length and varying beam width. Solid curves are for zero idler absorption and dashed curves are for α=300 m⁻¹.

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Fig. 9

Simulation results for 0.5 mm beam radius and 10 ns pulse length with a) 30% and b) 80% signal reflectivity on the output mirror in the OPO. The curves can be compared to Fig. 3b for 50% output coupling.

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Fig. 11

Fractional heat load as function of signal conversion efficiency.

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Fig. 12

Comparison of OPOs simulated with and without transient thermal lensing. W = 1 mm, α = 300 m⁻¹ and t_p = 20 ns. K = 5×10⁻¹² J/m³ in the case of transient lensing. a) Comparison of performance. b-c) Comparison of temporal evolution of the near-field intensity profile through the beam center for d_eff = 12 pm/V.

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Fig. 13

Calculated performance from OPOs with idler absorption as function of pulse repetition frequency when thermal lensing is accounted for. a) W = 0.5 mm t_p = 10 ns, η(prf = 0) ~0.4. b) W = 1 mm t_p = 20 ns, η(prf = 0) ~0.4. For illustration, we have taken the values from single shot simulations and plotted them as 0.1 Hz in b).

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Tables (2)

Table 1 List of parameters used in the simulations

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Table 2 Original and scaled parameters for two realistic example OPOs. The columns labeled OPO 1 and OPO 2 show the physical parameters, and the columns labeled “scaled” show the parameters for the equivalent OPOs in our simulations. The shaded cells show the values we use to look up the expected efficiency and beam quality in our graphs

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Equations (13)

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\begin{matrix} \frac{d a_{1}}{d z} = i ω_{1} γ a_{3} a_{2}^{*} \exp (i Δ k \times z) - \frac{α_{1} a_{1}}{2} \\ \frac{d a_{2}}{d z} = i ω_{2} γ a_{3} a_{1}^{*} \exp (i Δ k \times z) - \frac{α_{2} a_{2}}{2} \end{matrix},

γ = 2 d_{e f f} / \sqrt{2 n_{3} n_{2} n_{1} c^{3} ε_{0}},

g = \frac{1}{2} (- \frac{α_{2}}{2} - \frac{α_{1}}{2} + i Δ k + \sqrt{4 {(γ \bar{ω} a_{3})}^{2} + {(\frac{α_{2}}{2} - \frac{α_{1}}{2} + i Δ k)}^{2}}),

g = \frac{1}{2} (- \frac{α_{1}}{2} + \sqrt{4 {(γ \bar{ω} a_{3})}^{2} + \frac{α_{1}^{2}}{4}}) \approx {\begin{matrix} γ \bar{ω} a_{3} - α_{1} / 4 for high gain (γ \bar{ω} a_{3} > > α_{1}) \\ 2 {(γ \bar{ω} a_{3})}^{2} / α_{1} for high gain (γ \bar{ω} a_{3} < < α_{1}) \end{matrix}

\begin{array}{l} \frac{\partial a_{1}}{\partial z} = \frac{- i}{2 k_{1}} \nabla_{T}^{2} a_{1} + i ω_{1} γ a_{3} a_{2}^{*} - \frac{α_{1}}{2} a_{1} \\ \frac{\partial a_{2}}{\partial z} = \frac{- i}{2 k_{2}} \nabla_{T}^{2} a_{2} + i ω_{2} γ a_{3} a_{1}^{*} \\ \frac{\partial a_{3}}{\partial z} = \frac{- i}{2 k_{3}} \nabla_{T}^{2} a_{3} + i ω_{3} γ a_{1} a_{2} \end{array},

L_{d} = k_{3} W^{2},

σ = a_{0, 3} ω_{3} γ

\begin{matrix} \frac{1}{L_{c}} \frac{\partial A_{1}}{\partial z'} = \frac{- i}{2 β L_{d}} \nabla_{T}^{2} A_{1} + i β σ A_{3} A_{2}^{*} - \frac{α_{1}}{2} A \\ \frac{1}{L_{c}} \frac{\partial A_{2}}{\partial z'} = \frac{- i}{2 β L_{d}} \nabla_{T}^{2} A_{2} + i (1 - β) σ A_{3} A_{1}^{*} \\ \frac{1}{L_{c}} \frac{\partial A_{3}}{\partial z'} = \frac{- i}{2 β L_{d}} \nabla_{T}^{2} A_{3} + i σ A_{1} A_{2} \end{matrix} .

\begin{array}{l} α_{1} = α_{1}' s \\ σ = σ' s \\ L_{d} = L_{d}' / s \end{array},

\begin{matrix} t_{r} = 2 L_{c} n / c \\ N_{r t} = t_{p} / t_{r} \end{matrix} .

I_{0, 3} = I_{0} {(t_{p} / t_{0})}^{- 1 / 2},

f_{T} = \frac{2 κ}{Q L_{c} d n / d T},

F_{\max} \approx \frac{κ λ}{π W^{2} q L_{c} d n / d T} .

Parameter	Unit	Comment	Value
Pump radius	mm	e⁻²M	0.05-1
Pump pulse length	ns	FWHM	2-50
Pump wavelength	µm		1.064
Pump bandwidth			SLM
Signal wavelength	µm		1.6
Idler wavelength	µm		3.176
Idler absorption	m⁻¹		0-400
Effective nonlinearity	pm/V		2-40
Mirror curvatures			Flat
Mirror 1 reflectivity		i,s,p	0,1,0
Mirror 2 reflectivity		i,s,p	0,0.5,0
Refractive index		i,s,p	1.7,1.7,1.7
Group index		i,s,p	1.7,1.76,1.73
Crystal length	mm		10

Parameter	Unit	OPO 1	OPO 1 scaled	OPO 2	OPO 2 scaled
Material		KTP		PPLN
L_c	mm	20		15
λ ₃, n ₃	µm	1.064, 1.75		1.52, 2.14
λ ₂, n ₂	µm	1.571, 1.73		2.13, 2.12
λ ₁, n ₁	µm	3.298, 1.77		5.30, 1.98
S		2		1.5
σ’	m⁻¹	203	406	372	558
α ₁ '	m⁻¹	52	104	120	180
N_rt’		130	130	94	94
L_d’	m	10.3	5.2	0.80	0.53
t_p	ns	30	14.7	20	10.7
d_eff	pm/V	2.9	7.7	11	8.3
W_p	mm	1.0	0.7	0.3	0.23

Parameter	Unit	Comment	Value
Pump radius	mm	e⁻²M	0.05-1
Pump pulse length	ns	FWHM	2-50
Pump wavelength	µm		1.064
Pump bandwidth			SLM
Signal wavelength	µm		1.6
Idler wavelength	µm		3.176
Idler absorption	m⁻¹		0-400
Effective nonlinearity	pm/V		2-40
Mirror curvatures			Flat
Mirror 1 reflectivity		i,s,p	0,1,0
Mirror 2 reflectivity		i,s,p	0,0.5,0
Refractive index		i,s,p	1.7,1.7,1.7
Group index		i,s,p	1.7,1.76,1.73
Crystal length	mm		10

Parameter	Unit	OPO 1	OPO 1 scaled	OPO 2	OPO 2 scaled
Material		KTP		PPLN
L_c	mm	20		15
λ ₃, n ₃	µm	1.064, 1.75		1.52, 2.14
λ ₂, n ₂	µm	1.571, 1.73		2.13, 2.12
λ ₁, n ₁	µm	3.298, 1.77		5.30, 1.98
S		2		1.5
σ’	m⁻¹	203	406	372	558
α ₁ '	m⁻¹	52	104	120	180
N_rt’		130	130	94	94
L_d’	m	10.3	5.2	0.80	0.53
t_p	ns	30	14.7	20	10.7
d_eff	pm/V	2.9	7.7	11	8.3
W_p	mm	1.0	0.7	0.3	0.23

Abstract

References

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Wang, S.

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Proc. SPIE (1)

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